Categorical/Conditional Syllogisms

Question 1

All Raptors fans like watching basketball.
Chloe is a Raptors fan.
Ergo, Chloe likes watching basketball.

Answer 1

Valid: No rules violated

Question 2

All Raptors fans like watching basketball.
Chloe likes watching basketball.
Ergo, Chloe is a Raptors fan.

Answer 2

Invalid: the middle term must be distributed at least once. (Rule 3)

Question 3

No liar is truly happy.
Some politicians are liars.
Ergo, no politician is truly happy.

Answer 3

Invalid: the number of universal premises must be exactly one more than the number of universal conclusions. (Rule 2)

Question 4

L > M
~ L
Ergo, ~M

Answer 4

Invalid: the minor premise denies the antecedent (DA)

Question 5

All X are Y.
Some X are Z.
All Y are Z.

Answer 5

Invalid: Any term which is distributed in the conclusion must also be distributed in the premises (Rule 4)

Question 6

All cobras are poisonous.
Some spiders are poisonous.
Ergo, some spiders are cobras.

Answer 6

Invalid: the middle term must be distributed at least once. (Rule 3)

Question 7

No L is M.
Some M are not N.
Erog, some N are not L.

Answer 7

Invalid: from two negative premises, no conclusion can be drawn.

Question 8

All A are B.
Some C are not B.
Ergo, some C are not A.

Answer 8

Valid: No rules violated.

Question 9

Some introverts prefer to be quiet.
Some extroverts are not quiet.
Ergo, some introverts are extroverts.

Answer 9

Invalid: If a premise is particular, than the conclusion must be particular. If a premise is negative, than the conclusion must be negative. (Rule 6).

Question 10

If you have a lax conscience, then you will not help someone in need.
You helped a student who was struggling with logic problems.
Therefore, you do not have a lax conscience.

Answer 10

Valid: The minor premise denies the consequent (DC)

Question 11

All friendly greetings are appreciated.
Some compliments are not appreciated.
Ergo, some compliments do not qualify as friendly greetings.

Answer 11

Valid: no rules violated.

Question 12

All M are N.
Some N are O.
Ergo, all M are O.

Answer 12

Invalid: the middle term must be distributed at least once. (Rule 3)

Question 13

Some brave people are firefighters.
Jamal is a firefighter.
Therefore, Jamal is brave.

Answer 13

Invalid: The middle term must be distributed at least once (Rule 3).

Question 14

If you eat too much sugar, you are putting yourself at risk of diabetes.
You do not eat too much sugar.
Therefore, you are not at risk of diabetes.

Answer 14

Invalid: The minor premise denies the antecedent (DA).

Question 15

If Charlie Brown wants to kick the football, then lucy will have to hold it for him.
Lucy does not hold it for him.
Therefore, Charlie Brown will not be able to kick the football.

Answer 15

Valid: The minor premises denies the consequent (DC).

Question 16

Some passive individuals are persons who live will because, some passive individuals are not worriers and some folks who live well are worriers.

Answer 16

Invalid: If a premise is particular, then the conclusion is particular. If a premise is negative, then the conclusion is negative (Rule 6).

Question 17

Some pirates are mercenaries; hence, some sailors are pirates, because all sailors are mercenaries.

Answer 17

Invalid: the middle term must be distributed at least once (Rule 3).

Question 18

If a driver is caught speeding, that person will be ticketed by police.
This driver was caught speeding.
Therefore, this driver will be ticketed by police.

Answer 18

Valid: The minor premise affirms the antecedent (AA).

Question 19

If you have been paying attention, then this quiz was easy.
This quiz was easy.
Ergo, you have been paying attention.

Answer 19

Invalid: the minor premise affirms the consequent (AC)

Question 20

If you have been paying attention, then this quiz was easy.
You have not been paying attention.
Ergo, this quiz was difficult.

Answer 20

Invalid: the minor premise denies the antecedent (DA)

Question 21

All cats like tuna.
Some humans like tuna.
Ergo, some humans are cats.

Answer 21

Invalid: Middle term is not distributed (rule 3)

Question 22

A, D.
~A.
Ergo, ~D.

Answer 22

Invalid: The minor premise denies the antecedent (DA).

Question 23

No penguins can fly.
Some turkeys can not fly.
Ergo, some turkeys are penguins.

Answer 23

Invalid: two negative premises cannot have a conclusion (rule 1).

Question 24

Some A are C.
All C are B.
Ergo, some A are B.

Answer 24

Valid: no rules violated

Question 25

Some D are E.
All E are F.
Ergo, all D are F.

Answer 25

Invalid: the terms in the conclusion must be distributed in the premise (rule 4).

Question 26

T>P.
~T.
Ergo, ~P.

Answer 26

Invalid: the minor premise denies the antecedent (DA)

Question 27

All dogs like treats.
I like treats.
Ergo, I am a dog.

Answer 27

Invalid: the middle term is not distributed (rule 3).

Question 28

Some singers are dancers.
Some actors are dancers.
Ergo, all singers are actors.

Answer 28

Invalid: the premises are not universal statements (rule 2).

Question 29

All D are E.
Some E are not F.
Ergo, some D are not F.

Answer 29

Invalid: the middle term is not distributed.

Question 30

If you practice, you will improve.
You did not practice.
Ergo, you did not improve.

Answer 30

Invalid: the minor premise denies the antecedent (DA).